Simplify the following expression: $n = \dfrac{9r^2 - 54r + 45}{r - 5} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ n =\dfrac{9(r^2 - 6r + 5)}{r - 5} $ Then we factor the remaining polynomial: $r^2 {-6}r + {5} $ ${-5} {-1} = {-6}$ ${-5} \times {-1} = {5}$ $ (r {-5}) (r {-1}) $ This gives us a factored expression: $\dfrac{9(r {-5}) (r {-1})}{r - 5}$ We can divide the numerator and denominator by $(r + 5)$ on condition that $r \neq 5$ Therefore $n = 9(r - 1); r \neq 5$